The height in feet of a rocket after t seconds is given by h(t) = 160t - 16t2.
Find the maximum height the rocket attains:
After how many seconds does it reach this height?
-16x^2 + 160t
The max. point on the parabola is the vertex:
t = Xv = -B/2A = -160/-32 5 s
hmax. = Yv = -16*5^2 + 160*5 = 400 Ft.
V(5,400).
To find the maximum height the rocket attains, we need to determine the vertex of the quadratic function h(t) = 160t - 16t^2. The vertex represents the highest point on the graph and corresponds to the maximum height.
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic function.
In this case, the quadratic function is h(t) = -16t^2 + 160t, so a = -16, b = 160, and c = 0.
The t-coordinate of the vertex is -b/2a. Plugging in the values, we get:
t = -160 / (2(-16))
t = -160 / (-32)
t = 5
So, the maximum height is reached after 5 seconds.
To calculate the maximum height the rocket attains, we need to substitute this value of t into the quadratic function h(t):
h(5) = -16(5)^2 + 160(5)
h(5) = -16(25) + 800
h(5) = -400 + 800
h(5) = 400
Therefore, the maximum height the rocket attains is 400 feet and it reaches this height after 5 seconds.